Daniel Beltita

Coadjoint dynamical systems and group C*-algebras

We approach some basic topological properties of unitary dual spaces of solvable Lie groups using suitable dynamical systems defined by the coadjoint action.
For any exponential solvable Lie group the method of coadjoint orbits still works
and we use it for computing some noncommutative dimensions (the real and stable rank) of the group C*-algebra in terms of the Lie algebra of the group under consideration. Beyond that class of groups, we construct an example of solvable Lie group whose unitary dual space contains a dense singleton subset.